6.1 solving systems of equations by graphing. evaluate each expression for x = 1 and y = –3. 1. x...
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6.1 Solving Systems Of Equations By Graphing
Evaluate each expression for x = 1 and y = –3.
1. x – 4y 2. –2x + y
Write each expression in slope-intercept form.
3. y – x = 1
4. 2x + 3y = 6
5.
Bell Work
Bolt=
Cheetah=
Time
Distance
100 m
9 10
(5.95, 100) (9.58,
100)
Bolt=
Cheetah=
Time
Distance
100 m
9 10
(9.58, 100)
40 m
Solving Linear Equations By Graphing
• Our goal is to;
1. Graph TWO lines on same graph
2. Locate where they intersect (or if they do at all)
Solving a Linear Equation
• Linear equations can look like;
y = 3x + 7Or
-3x + y = 7Or
7 + 3x = yOr…
3 Graphing Possibilities
1.Intersecting Lines
2.Parallel Lines
3.Coinciding Lines
1) Intersecting Lines
• The point where the lines intersect is your solution.
• The solution of this graph is (1, 2)
(1,2)
What is the solution of the system graphed below?
1. (2, -2)2. (-2, 2)3. No solution4. Infinitely many
solutions
Where do these graphs intersect
2) Parallel Lines
• These lines never intersect!
• Since the lines never cross, there is NO SOLUTION!
• Parallel lines = SAME SLOPE, different y-int.
2Slope = = 2
1y-intercept = 2
y-intercept = -1
Parallel Lines
Hi, I’m Two
Hey, I’m Two Too!Our Slopes
Must Be Twins!!!
What is the solution of this system?
y = 3x + 3y = 3x - 12
1. (3, -12)2. Parallel solutions3. No solution4. Infinitely many
solutions
3) Coinciding Lines
• These lines are the same!
• Since the lines are on top of each other, there are INFINITELY MANY SOLUTIONS!
• Coinciding lines = SAME SLOPE, SAME Y-INT.
2Slope = = 2
1y-intercept = -1
What is the solution of this system?
y = 3x - 8 y = 3x - 8
1. (3, 1)2. (4, 4)3. No solution4. Infinitely many
solutions
Lets try one: Find the solution to the following system:
y = -2x+4 y = x -2
Step 1:Graph both equations
m=-2 b=4
m=1 b=-2
Step 2: Find Where the lines intersect?
THE SOLUTION: (2,0)
You try: Where do the lines intersect?
Graph both equations
Where do they intersect?
y = 2x – 1y = –x + 5
The point is (2, 3)
Try again: Find the solution to the system
Graph both equations
NO SOLUTION
y = -2x+4
y = -2x-1
Where do they intersect?
Find the Solution
Summary
• Intersecting Lines have how many solutions?
• Parallel Lines have the same what?• How can you tell if two equations are
coinciding without graphing them?• Do you have to graph the system to
know the answer if both equations have the same slope?
HOMEWORK
• Find an example in real life (just like Usain Bolt vs. Cheetah) and graph it.
– I want to see the following1. What two things are you graphing2. What is your x-axis and y-axis3. Graph them4. Do they intersect? Where?